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# If ab = b, which of the following must be true?

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Manager
Joined: 28 Jun 2018
Posts: 153
Location: India
Concentration: Finance, Marketing
Schools: CUHK '21 (II)
GMAT 1: 650 Q49 V30
GPA: 4
If ab = b, which of the following must be true?  [#permalink]

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27 Aug 2018, 01:11
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57% (00:50) correct 43% (00:47) wrong based on 63 sessions

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If ab = b, which of the following must be true?

A) a=1
B) b=0
C) a=1 and b=0
D) a=1 or b=1
E) a=1 or b=0

_________________
Math Expert
Joined: 02 Aug 2009
Posts: 7764
Re: If ab = b, which of the following must be true?  [#permalink]

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27 Aug 2018, 01:16
1
1
GMATbuster92 wrote:
if ab=b , which of the following must be true?
A) a=1
B) b=0
C) a=1 and b=0
D) a=1 or b=1
E) a=1 or b=0

$$ab=b........ab-b=0........b(a-1)=0$$
so a=1 or b=0 or both

E
_________________
IESE School Moderator
Joined: 11 Nov 2017
Posts: 118
Location: Belgium
Concentration: Technology, Operations
GMAT 1: 670 Q47 V34
GMAT 2: 750 Q50 V41
GMAT 3: 750 Q50 V41
GPA: 2.5
WE: Engineering (Aerospace and Defense)
Re: If ab = b, which of the following must be true?  [#permalink]

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27 Aug 2018, 01:20
fairly straightforward:

ab=b

any number multiplied by 1 remains the same:
1.b=b
--> a=1
there is no other option for a to be anything else since that would modify the outcome

then ask yourself: is there an option where b on it's own can make this true:
the only case where any variable number of times a number = that number is for 0
1.b=b
2.b=b
3.b=b
is only ever true for b=0

since we figured out these 2 requirements a=1, b=0 separately, this means there is no dependency, hence:
OR

a=1 or b=0

--> E

kudos if this helped
Senior Manager
Joined: 12 Sep 2017
Posts: 295
If ab = b, which of the following must be true?  [#permalink]

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04 Mar 2019, 15:29
Hello everyone!

Could someone give some detailed explanation regarding the difference between AND/OR?

$$ab = b$$

$$b (a - 1) = 0$$

$$b = 0$$
$$a = 1$$

Kind regards!
If ab = b, which of the following must be true?   [#permalink] 04 Mar 2019, 15:29
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# If ab = b, which of the following must be true?

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